Econ 200H: David Reiley
Due Tuesday, 10 October 2006
Problem Set #3
As before, the following exercises come from the end-of-chapter problems in
the Taylor textbook. Recall that in general, I recommend not spending more than
about 20 minutes thinking about any single problem. (The extra-credit problems
are an exception - I expect them to take longer, but they are an opportunity
for those who are interested in learning more.)
- (10 points) Taylor, problem 8.2.
- (10 points) Taylor, problem 8.5.
- (10 points) (This is a rewritten version of Taylor, problem 8.4.) Suppose the firm in problem 3 adds an additional machine, which changes the short-run average-cost curve so that the minimum AC is 10. Does this imply long-run economies of scale, or diseconomies of scale? Explain your answer by sketching what the two different short-run average cost curves might look like.
- (20 points) Taylor, problem 8.6.
- (20 points) Taylor, problem 8.7.
- (10 points) Explain why P=MC in the short-run equilibrium for a perfectly
competitive firm, whereas in the long run P=MC=AC.
- (10 points) If the firm's lowest average cost is $48 and its lowest average
variable cost is $24, what does it pay a perfectly competitive firm to do
- the market price is $49?
- the market price is $30?
- the market price is $8?
- (10 points) The firm's MC curve goes through the lowest point of its ATC
curve and also through the lowest point of its AVC curve. But the AVC curve
lies below the AC curve, so how can both of these statements be true? Why
are they true?
- (10 points) Taylor, problem 9.1.
- (10 points) Taylor, problem 9.4.
- (5 points) Taylor, problem 9.6.
- (10 points) Taylor, problem 9.7.
- (10 points) Taylor, problem 9.8.
- (20 points) Taylor, problem 9.10.
- (10 points) Taylor, problem 10.1.
- (10 points) Taylor, problem 10.4.
- (10 points) Taylor, problem 10.5.
- (15 points) Taylor, problem 10.7.
- (10 points) Taylor, problem 10.9. Note: In this problem you may run into
uncertainty because the table only gives values for even numbers of quantity
units. Assume that the good in question is something sold in pairs, like shoes,
so that you can't sell an odd number.
- (20 points) Taylor, problem 10.10. Note: there is an error in this problem.
In addition to "showing" the loss of consumer surplus and the deadweight loss
on your graph, please also compute the values of these amounts.
- (20 points) In this problem, we will demonstrate the result
described in footnote 1 on page 251 of the text. Suppose there is a
monopoly seller for chocolate shakes on campus, and she faces the
demand curve Q=100-10P.
- What is the price when the monopolist sells just one shake? Use this
information to compute the marginal revenue for the first unit sold.
- What is the price when the monopolist sells two shakes? Use this
information to compute the marginal revenue for the second unit sold.
- Consider the prices at which the monopolist could sell either 20 or
21 shakes. Use these to compute the marginal revenue for the 21st unit
- Similarly, compute the marginal revenue for the 22nd unit sold.
- Similarly, compute the marginal revenue for the 51st unit sold.
- Plot the demand curve. On this same graph, plot the five points you
have computed above. Connect these dots to produce a marginal-revenue
- What is the equation of this marginal-revenue curve as a function of
Note that, as described in footnote 1, the monopolist is facing a linear
demand curve, and therefore the MR curve is also linear, starting at approximately
the same price as the demand curve starts when Q=0, and decreasing with
twice the slope of the demand curve as Q increases. The reason this is
only approximately true is that we're working with discrete instead of
continuously divisible units. (One can prove this result, which is true
for all linear demand curves, using calculus.)
- (10 points) Suppose that a monopoly seller of footballs can profitably sell
at different prices in two different markets: high school and college. High-school
students have perfectly elastic demand at a price of $4. College students
have downward-sloping demand: Q=100-10P.
- If the monopolist is price-discriminating optimally, what must be true
of marginal revenues in the two different markets?
- Even without knowing the monopolist's cost curves, it is possible in
this situation to figure out what the prices should be in the two different
markets. You'll need to use the marginal-revenue result from the previous
problem. What should the two prices be?
- (20 points) Visit my Market.Econ
Web site. Sign up for an account on the site, and then play at least five
10-period games of the Potato Wafer Game. The total points you earn on this
exercise will be determined by the % of cumulative profits you earn, averaged
across all games you play. You may play as many games as you like in an effort
to raise your average.
- (Optional - 15 extra-credit points) Read the Appendix to Chapter 8, on Producer
Theory with Isoquants, and answer problems 8A.1.-8A.3.
- (Optional - 20 extra-credit points). Every time you play the Potato Wafer
Game, the demand curve has a linear form: Q = a - b P, where a
and b are numbers chosen at random. In addition, you face fixed costs
of size F and marginal costs of size c per unit produced. (In
every game, F = $2 million, and c = $0.75.) Your assignment
in this extra-credit problem is to derive a formula for the optimal price.
Your answer should be an equation that relates the optimal price P*
to the parameters a, b, c, and F.
After deriving the correct formula, please indicate how the optimal price
changes when a increases, when b increases, when c increases, and when F increases.
(Hint #1: You will want to use calculus to derive this formula.)
(Hint #2: This can be done by referring to what we've learned in the text,
but it is easy to become confused about what the "margin" is. Remember
that "marginal revenue" is the change in revenue with respect to
a change in quantity, not price.)
(Hint #3: It is possible to derive the correct formula without referring to
the text, so long as you understand the profit-maximization problem well and
know how to use calculus.)
- (Optional - 10 extra-credit points). Provide evidence of a specific example
of price discrimination. (Note that two different firms charging two different
prices is not price discrimination. Price discrimination involves a single
firm charging different prices to different customers.). Your evidence might
be a newspaper article, a couple of online advertisements, or a couple of
receipts showing different prices for the same product, for example. Describe
what sort of price discrimination is going on, and which type of customer
is paying which price.